The correct roots of the equation are (a) 9 and 1
From the complete question, their mistakes are:
Anu
- Roots: 8 and 2
- Wrong constant term
Aji
- Roots: -9 and -1
- Wrong coefficient
A quadratic equation is represented as:
[tex]ax^2 + bx + c = 0[/tex]
Where:
[tex]\alpha\beta = \frac ca[/tex] --- product of roots
[tex]\alpha + \beta = -\frac ba[/tex] --- sum of roots
Anu made a mistake in the constant term, so we consider the sum of roots
[tex]Sum = 8 + 2[/tex]
[tex]Sum = 10[/tex]
Aji made a mistake in the coefficient, so we consider the product of roots
[tex]Product = -9 \times -1[/tex]
[tex]Product = 9[/tex]
The possible equations from the above sum and products are:
- [tex]x^2 + 10x + 9 =0[/tex].
- [tex]x^2 - 10x + 9 =0[/tex].
- [tex]x^2 + 10x - 9 =0[/tex].
- [tex]x^2 - 10x - 9 =0[/tex]
Of all the above equations, the most likely equation is [tex]x^2 - 10x + 9 =0[/tex], and it has a root of 9 and 1
Hence, the correct roots are (a) 9 and 1
Read more about roots of equations at:
https://brainly.com/question/3923172
